objectives gases - youngbull science center -...

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THE BIG

IDEA ......

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How Can You Levitate an Object?1. Bend the elbow of a flexible straw approxi-

mately 90°.

2. Place the long section of the straw in your mouth and hold a table tennis ball a few cen-timeters above the short section.

3. Blow steadily through the straw as you release the ball. Keep trying until the ball levitates.

4. While still blowing, increase the angle between the long and short sections of the straw so that the air stream is not directly beneath the ball.

Analyze and Conclude1. Observing What happened when the air

stream was no longer directly beneath the ball?

2. Predicting How large can the angle between the two sections of the straw be if the ball is to remain suspended?

3. Making Generalizations What keeps the ball suspended when the air stream is not directly beneath the ball?

discover!

GASES

Gases are similar to liquids in that they flow; hence both are called fluids. The primary difference between gases

and liquids is the distance between mol-ecules. In a liquid, the molecules are close together, where they continually experience attractive forces from the surrounding mol-ecules. These forces strongly affect the motion of the molecules. In a gas, the molecules are far apart, allowing them to move freely between col-lisions. When two molecules in a gas collide, if one gains speed in the collision, the other loses speed, such that their total kinetic energy is unchanged.

A gas expands to fill all space available to it and takes the shape of its container. Only when the quantity of gas is very large, such as in Earth’s atmosphere or in a star, does gravitation determine the shape of the gas.

Gas molecules are far apart and can move freely between collisions.

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GASESObjectives• Describe Earth’s atmosphere.

(20.1)

• Explain what causes atmospheric pressure. (20.2)

• Describe how a simple mercury barometer shows pressure. (20.3)

• Explain how an aneroid barometer works. (20.4)

• Describe the relationship between the pressure and volume for a given mass of gas at a constant temperature. (20.5)

• Explain what causes an object to rise in the air around it. (20.6)

• Describe the relationship between the speed of a fluid at any point and the pressure at that point, for steady flow. (20.7)

• Explain how horizontal flight is possible. (20.8)

discover!

MATERIALS flexible straw, table tennis ball

EXPECTED OUTCOME The students will observe that they can levitate the ball with an air stream.

ANALYZE AND CONCLUDE

The ball hovered beside the air stream.

For a light ball with a fast air stream, the ball can levitate at an angle of about 30°.

When air moves faster on one side of the ball than the other, pressure is reduced there and the ball is pushed toward the stream. Part of the air stream that impacts the bottom of the ball keeps it from falling.

1.

2.

3.

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20.1 The AtmosphereWe don’t have to look far to find a sample of gas. We live in an ocean of gas, our atmosphere. Earth’s atmosphere consists of molecules that occupy space and extends many kilometers above Earth’s sur-face. The molecules are energized by sunlight and kept in continual motion like the gas molecules shown in Figure 20.1. Without Earth’s gravity, they would fly off into outer space. And without the sun’s energy, the molecules would eventually cool and just end up as mat-ter on the ground. Fortunately, because of an energizing sun and because of gravity, we have an atmosphere.

Unlike the ocean, which has a very definite upper surface, Earth’s atmosphere has no definite upper surface. And unlike the ocean’s uniform density at any depth, the density of the atmosphere decreases with altitude. Molecules in the atmosphere are closer together at sea level than at higher altitudes. The atmosphere is like a huge pile of feathers, where those at the bottom are more squashed than those nearer to the top. The air gets thinner and thinner (less dense) the higher one goes; it eventually thins out into space.

Even in the vacuous regions of interplanetary space there is a gas density of about one molecule per cubic centimeter. This is primarily hydrogen, the most plentiful element in the universe.

Figure 20.2 shows how thin our atmosphere is. Note that 50% of the atmosphere is below 5.6 kilometers (18,000 ft), 75% of the atmosphere is below 11 kilometers (56,000 ft), 90% of the atmosphere is below 17.7 kilo-meters, and 99% of the atmosphere is below an altitude of about 30 kilo-meters. Compared with Earth’s radius, 30 kilometers is very small. To give you an idea of how small, the “thickness” of the atmosphere relative to the size of the world is like the thickness of the skin of an apple relative to the size of the apple. Our atmosphere is a delicate and finite life-sustaining thin shell of air; that’s why we should care for it.

CONCEPTCHECK ...

... What is the atmosphere?

FIGURE 20.1 �Molecules in the gaseous state are in continuous motion.

FIGURE 20.2 �The temperature of the atmosphere drops as one goes higher (until it rises again at very high altitudes).

CHAPTER 20 GASES 383

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20.1 The Atmosphere

Common Misconception The atmosphere of Earth extends upward for hundreds of kilometers.

FACT 99% of Earth’s atmosphere is below an altitude of 30 km.

� Teaching Tip Draw a large circle on the chalkboard to represent Earth. State that if you were to draw another circle, indicating the thickness of the atmosphere surrounding Earth to scale, you would end up drawing the same line—for over 99% of the atmosphere lies within the thickness of the chalk line! (We compare a 30-km depth of atmosphere to Earth’s radius 6370 km.)

Earth’s atmosphere consists of molecules

that occupy space and extends many kilometers above Earth’s surface.

T e a c h i n g R e s o u r c e s

• Reading and Study Workbook

• Transparency 36

• PresentationEXPRESS

• Interactive Textbook

• Next-Time Question 20-1

• Conceptual Physics Alive! DVDs Gases

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The concepts of fluid pressure, buoyancy, and flotation introduced in the previous chapter are applied to the atmosphere in this chapter. You should point out that unlike a liquid, the density of the atmosphere is depth-dependent. It thins with increasing altitude.


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20.2 Atmospheric PressureWe live at the bottom of an ocean of air. The atmosphere, much like water in a lake, exerts pressure. Atmospheric pressure is caused by the weight of air, just as water pressure is caused by the weight of water. We are so accustomed to the invisible air around us that we sometimes forget it has weight. Perhaps a fish “forgets” about the weight of water in the same way. Figure 20.3 illustrates this point.

Gas

Table 20.1 Densities of Various Gases

Density (kg/m3)*

Dry air

0º C

10° C

20° C

30° C

Helium

Hydrogen

Oxygen* At sea level atmospheric pressure and at 0° C (unless otherwise specified)

1.29

1.25

1.21

1.16

0.178

0.090

1.43

Table 20.1 shows how the density of air changes with tempera-ture. At sea level, 1 cubic meter of air at 20°C has a mass of about 1.2 kg. Calculate the number of cubic meters in your room, multiply by 1.2 kg/m3, and you’ll have the mass of air in your room. Don’t be surprised if it has more mass than your kid sister. Air is heavy if you have enough of it. For example, it takes more than 1800 kg of air to pressurize the jet shown in Figure 20.4.

FIGURE 20.3 �You don’t notice the weight of a bag of water while you’re submerged in water. Similarly, you don’t notice the weight of air as you walk around in it.

FIGURE 20.4 �Fully pressurizing a 777 jumbo jet adds 1800 kg to its mass.

Air is heavy if you have enough of it.


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20.2 Atmospheric Pressure

Common Misconception Air has no weight.

FACT At sea level, 1 m3 of air has a mass of about 1.2 kg and weighs about 11.7 N.

Caution: Wear goggles and heat-resistant gloves while performing this demonstration. Heat an aluminum soda can on a burner, empty except for a small amount of water that is brought to a boil to make steam. With a pot holder or tongs, pick up the can and quickly invert it into a basin of water. Crunch! The atmospheric pressure immediately crushes the can with a resounding WHOP! Very impressive. Condensation of the steam and vapor occur and the interior pressure is reduced. This occurs even when the temperature of the water bath into which the can is inverted is nearly boiling. What happens is a “flypaper effect”—water molecules in the vapor state condense when they encounter the water into which they’re placed—even hot water.

Ask Imagine a large grapefruit inside a refrigerator. Which weighs more, the air in the fridge or the grapefruit? The inside volume of a common refrigerator is between 1/2 and 3/4 m3, which corresponds to nearly 1 kg of cold air (about 2 lb). So unless the grapefruit is heavier than a 2-pounder, the air weighs more.

DemonstrationDemonstration


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About how many kilo-grams of air occupy a classroom that has a 200-square-meter floor area and a 4-meter-high ceiling?Answer: 20.2

think!If your kid sister doesn’t believe air has weight, maybe it’s because she’s surrounded by air all the time. Hand her a plastic bag of water and she’ll tell you it has weight. But hand her the same bag of water while she’s submerged in a swimming pool, and she won’t feel its weight because the bag is surrounded by water.

Consider a superlong hollow bamboo pole, like the one shown in Figure 20.5, that reaches up through the atmosphere for 30 kilo-meters. Suppose the inside cross-sectional area of the pole is 1 square centimeter. If the density of air inside the pole matches the density of air outside, the enclosed mass of air would be about 1 kilogram. The weight of this much air is about 10 newtons. So air pressure at the bottom of the bamboo pole would be about 10 newtons per square centimeter (10 N/cm2). Of course, the same is true without the bam-boo pole.

There are 10,000 square centimeters in 1 square meter. So a column of air 1 square meter in cross section that extends up through the atmosphere, as illustrated in Figure 20.6, has a mass of about 10,000 kilograms. The weight of this air is about 100,000 new-tons (105 N). This weight produces a pressure of 100,000 newtons per square meter, or equivalently, 100,000 pascals, or 100 kilopascals. More exactly, the average atmospheric pressure at sea level is 101.3 kilopas-cals (101.3 kPa).20.2

The pressure of the atmosphere is not uniform. Aside from variations with altitude, there are variations in atmospheric pres sure at any one locality due to moving air currents and storms. Measure-ment of changing air pressure is important to meteorologists in pre-dicting weather.

CONCEPTCHECK ...

... What causes atmospheric pressure?

� FIGURE 20.5The mass of air that would occupy a bamboo pole that extends to the “top” of the atmosphere is about 1 kg. This air has a weight of 10 N.

FIGURE 20.6 �The weight of air that bears down on a 1-square-meter surface at sea level is about 100,000 newtons.

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� Teaching Tip Have students calculate the mass of air in their classroom. (The mass of air in a typical room is 5 m 3 5 m 3 3 m 3 1.2 kg/m3 5 90 kg—about 200 lb.)

� Teaching Tip State that the weight of the air in the bamboo pole (Figure 20.5) is the source of atmospheric pressure. Ask your class to imagine a 30-km tall sewer pipe of cross section 1 m2, filled with the air of the atmosphere. The enclosed air would weigh about 105 N. So if you draw a circle of 1 m2 around your chair, and ask for the weight of all the air in the atmosphere above, you should elicit a chorus of “105 N!” This is the atmospheric pressure at the bottom of our ocean of air. If your chair is located well above sea level, in mountain areas for example, then the weight of the atmosphere is correspondingly less (just as water pressure is less for a fish nearer the surface).

� Teaching Tip Estimate the force of the air pressure that collapsed the metal can—both for a perfect vacuum and for a case where the pressure difference is about half an atmosphere. Estimate the force of the atmosphere on a person. Estimate the surface area by approximating different parts of the body on the board—leg by leg, arm by arm, etc.

Atmospheric pressure is caused by the

weight of air, just as water pressure is caused by the weight of water.





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20.3 The Simple BarometerAn instrument used for measuring the pressure of the atmosphere is called a barometer. A simple mercury barometer is illustrated in Figure 20.7. A glass tube, longer than 76 cm and closed at one end, is filled with mercury and tipped upside down in a dish of mercury. The mercury in the tube runs out of the submerged open bottom until the level falls to about 76 cm. The empty space trapped above, except for some mercury vapor, is a vacuum. The vertical height of the mercury column remains constant even when the tube is tilted, unless the top of the tube is less than 76 cm above the level in the dish, in which case the mercury completely fills the tube.

Why does mercury behave this way? The explanation is similar to the reason a simple see-saw balances when the weights of people at its two ends are equal. The barometer “balances” when the weight of liquid in the tube exerts the same pressure as the atmosphere outside. Whatever the width of the tube, a 76-cm column of mercury weighs the same as the air that would fill a supertall 30-km tube of the same width. If the atmospheric pressure increases, then it will push the mercury column higher than 76 cm. The mercury is literally pushed up into the tube of a barometer by atmospheric pressure. Theheight of the mercury in the tube of a simple barometer is a mea-sure of the atmospheric pressure.

Could water be used to make a barometer? The answer is yes, but the glass tube would have to be much longer—13.6 times as long, to be exact. You may recognize this number as the density of mercury relative to that of water. A volume of water 13.6 times that of mer-cury is needed to provide the same weight as the mercury in the tube (or in the imaginary tube of air outside). So the height of the tube would have to be at least 13.6 times taller than the mercury column. A water barometer would have to be 13.6 � (0.76 m), or 10.3 m high—too tall to be practical.

Healthwise, mercury is a no-no, and is something you don’t want to play around with.

FIGURE 20.7 �In a simple mercury barometer, variations above and below the average column height of 76 cm are caused by variations in atmospheric pressure.


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20.3 The Simple Barometer

Key Term barometer

� Teaching Tip Ask your students why air pressure doesn’t crush their bodies. Tell them that the 10 N/cm2 pressure on every square centimeter of the outside surface of their bodies is matched with a pressure of 10 N/cm2 on the inside.

� Teaching Tip Students often doubt that mercury in a barometer having the diameter of a hose would go to the same height as a barometer having the diameter of a pencil. Emphasize that pressure is force per unit area; since the larger tube has a larger cross-sectional area, it can support a greater weight of mercury than the smaller tube.

� Teaching Tip Discuss Figure 20.8 in which the girl shows that soda cannot be drawn through a straw unless atmospheric pressure acts on the liquid surface. Help students to see that sucking is not a force. Point out that a vacuum has nothing in it and cannot exert a force. It is the high pressure around the vacuum that pushes something into the vacuum, not the “sucking” by the vacuum.

The vacuum pump that my brother and my sister-in-law are demonstrating in Figure 20.9 operates by atmospheric pressure on the surface of water in the well.


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The operation of a barometer is similar to the process of drink-ing through a straw, which is shown in Figure 20.8. By sucking, you reduce the air pressure in the straw that is placed in a drink. Atmospheric pressure on the liquid’s surface pushes liquid up into the reduced-pressure region. Strictly speaking, the liquid is not suckedup; it is pushed up the straw by the pressure of the atmosphere. If the atmosphere is prevented from pushing on the surface of the drink, as in the party trick bottle with the straw through the airtight cork stop-per, one can suck and suck and get no drink.

If you understand these ideas, you can understand why there is a 10.3-meter limit on the height water can be lifted with vacuum pumps. The old-fashioned farm-type pump shown in Figure 20.9 operates by producing a partial vacuum in a pipe that extends down into the water below. The atmo-spheric pressure exerted on the surface of the water simply pushes the water up into the region of reduced pressure inside the pipe. Can you see that even with a perfect vacuum, the maximum height to which water can be lifted is 10.3 meters?

CONCEPTCHECK ...

... How does a simple mercury barometer show pressure?

FIGURE 20.9 �The atmosphere pushes water from below up into a pipe that is evacuated of air by the pumping action.

discover!

How Can You Transfer Liquid With a Drinking Straw?1. Lower a drinking straw into a glass of water and place

your finger over the top of the straw.

2. What happens when you lift the straw out of the water?

3. Now lift your finger from the top of the straw. What happens?

4. Think Why didn’t the water fall out of the straw when you first lifted it out of the water?

� FIGURE 20.8You cannot drink soda through the straw unless the atmosphere exerts a pressure on the surround-ing liquid.


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� Teaching Tip When the plunger of the vacuum pump in Figure 20.9 is lifted, air pressure is reduced in the pipe that extends into the well (because the air is “thinned” as it expands to fill a larger volume). The greater atmospheric pressure on the surrounding surface of the well water pushes water up the pipe, causing the water to overflow at the spout.

The height of the mercury in the tube

of a simple barometer is a measure of the atmospheric pressure.





CONCEPTCHECK ...

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discover!

MATERIALS drinking straw, container of water

EXPECTED OUTCOME Students should observe that when they lift the straw out of the water with their finger over the top of the straw, the water does not fall out of the straw.

THINK Before the student lifts his or her finger from the top of the straw, the weight of the water is supported by atmospheric pressure against the bottom of the straw. When the finger is removed, atmospheric pressure on the top counteracts atmospheric pressure on the bottom. The weight of the water is not supported and it flows out.


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20.4 The Aneroid BarometerFigure 20.10 shows a popular classroom demonstration used to illus-trate atmospheric pressure. A can containing a little water is heated until steam forms. Then the can is capped securely and removed from the source of heat. There is now less air inside the can than before it was heated. (Why? Because when the water boils and changes to steam, the steam pushes air out of the can.) When the sealed can cools, the pressure inside is reduced because steam inside the can condenses to a liquid when it cools. The greater pressure of the atmosphere outside the can then proceeds to crush the can. The pressure of the atmosphere is even more dramatically shown when a 50-gallon drum is crushed by the same procedure.

A much more subtle application of atmospheric crushing is used in an aneroid barometer. An aneroid barometer is an instru-ment that measures variations in atmospheric pressure without a liquid. An example of an aneroid barometer is shown in Figure 20.11. This small portable instrument is more prevalent than the mercury barometer. An aneroid barometer uses a small metal box that is partially exhausted of air. The box has a slightly flexible lid that bends in or out as atmospheric pressure changes. The pressure dif-ference between the inside and outside is less drastic than that of the crushed can of Figure 20.10. Motion of the lid is indicated on a scale by a mechanical spring-and-lever system. Since atmospheric pressure decreases with increasing altitude, a barometer can be used to deter-mine elevation. An aneroid barometer calibrated for altitude is called an altimeter (“altitude meter”). Some of these instruments are sensi-tive enough to indicate changes in elevation of less than a meter.

CONCEPTCHECK ...

... How does an aneroid barometer work?

FIGURE 20.11 �Aneroid barometers work without liquids. a. Variations in atmospheric pressure are indicated on the face of the instrument. b. The spring-and-lever system can be seen in this cross-sectional diagram.

FIGURE 20.10 �Atmospheric pressure is used to crush a can. a. The can is heated until steam forms. b. The can is capped and removed from the heat. c. When the can cools, the air pressure inside is reduced.

a b c


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20.4 The Aneroid Barometer

Key Term aneroid barometer

� Teaching Tip Discuss earpopping in aircraft, and why cabin pressure is higher than atmospheric pressure at high altitudes.

Ask How would a barometer reading vary while ascending and descending in the elevator of a tall building? The reading would drop when ascending and rise when descending.

An aneroid barometer uses a

small metal box that is partially exhausted of air. The box has a slightly flexible lid that bends in or out as atmospheric pressure changes.



• Concept-Development Practice Book 20-1



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20.5 Boyle’s LawThe air pressure inside the inflated tires of an automobile is consid-erably more than the atmospheric pressure outside. The density of air inside is also more than that of the air outside. To understand the relationship between pressure and density, think of the molecules inside the tire.20.5.1

Inside the tire, the molecules behave like tiny table tennis balls, perpetually moving helter-skelter and banging against the inner walls. Their impacts on the inner surface of the tire produce a jittery force that appears to our coarse senses as a steady push. This pushing force averaged over a unit of area provides the pressure of the enclosed air.

Suppose there are twice as many molecules in the same volume. As illustrated in Figure 20.12, the air density is then doubled. If the molecules move at the same average speed—or, equivalently, if they have the same temperature—then to a close approximation, the number of collisions will double. This means the pressure is doubled. So pressure is proportional to density.

The density of the air can also be doubled by simply compressing the air to half its volume. We increase the density of air in a balloon when we squeeze it, and likewise increase air density in the cylinder of a tire pump when we push the piston downward. Consider the cylinder with the movable piston in Figure 20.13. If the piston is pushed downward so that the volume is half the original volume, the density of molecules will be doubled, and the pressure will cor-respondingly be doubled. Decrease the volume to a third its original value, and the pressure will be increased by three, and so on.

� FIGURE 20.13When the volume of gas is decreased, the density—and therefore pressure—are increased.

If you squeeze a balloon to one-third its volume, by how much will the pressure inside increase?Answer: 20.5.1

think!

� FIGURE 20.12When the density of the air in the tire is increased, the pressure is increased.


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20.5 Boyle’s Law

Key Term Boyle’s law

� Teaching Tip Mention that the tire pressure gauge at a gas station measures the difference in air pressure and not the absolute air pressure. A flat tire registers zero pressure on the gauge, but a pressure of about one atmosphere exists there. Gauges read “gauge” pressure—pressure greater than atmospheric pressure.

� Teaching Tip Discuss the compressed air breathed by scuba divers and in the diving bells used in underwater construction. Workers can construct bridge foundations and so forth in such devices. They are in an environment of compressed air. The air pressure in these devices is at least as much as the combined pressure of water and the atmosphere outside.

� Teaching Tip Discuss the reason for the difficulty of snorkeling at a depth of 1 m and why snorkeling will not work for greater depths, i.e., air will not move from a region of lesser pressure (the air at the surface) to a region of greater pressure (the compressed air in the submerged person’s lungs) without artificial means. To breathe, we depress our diaphragm to reduce lung pressure, so the atmospheric pressure outside ensures a flow of inward air. However, the increased pressure of the water beneath the surface results in a greater pressure in the lungs than in the atmosphere. Any flow of air is outward. That’s why pumps must be used to supply air to divers below the surface of water.


390

Notice from these examples that the product of pressure and volume is the same for any given quantity of a gas. For example, a doubled pressure multiplied by a halved volume gives the same value as a tripled pressure multiplied by a one-third volume. Boyle’s law describes the relationship between the pressure and volume of a gas.

Boyle’s law states that the product of pressure and volume for a given mass of gas is a constant as long as the temperature does not change. “Pressure � volume” for a sample of gas at one time is equal to any “different pressure � different volume” of the same sample of gas at any other time. In equation form,

P1V1 P2V2

where P1 and V

1 represent the original pressure and volume, respec-

tively, and P2 and V

2 the second, or final, pressure and volume. Boyle’s

law is named after Robert Boyle, the seventeenth-century physicist who is credited with its discovery.20.5.2

Scuba divers, such as the one in Figure 20.14, must be aware of Boyle’s law when ascending. As the diver returns to the surface, pressure decreases and thus the volume of air in the diver’s lungs increases. This is why a diver must not hold his or her breath while ascending—the expansion of the diver’s lungs beyond capacity can be very dangerous or even fatal.

CONCEPTCHECK ...

... What does Boyle’s law state?

Or Boyle’s law can look like this: PV = PV, or PV = PV.

FIGURE 20.14 �A scuba diver must be aware of Boyle’s law when ascending to the surface.

think!A scuba diver 10.3 m deep breathes com-pressed air. If she holds her breath while returning to the surface, by how much does the volume of her lungs tend to increase?Answer: 20.5.2

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� Teaching Tip Tell your students that in a chemistry class they’ll see the ideal gas law in the form PV 5 nRT, where n is the number of moles of gas (1 mole 5 6.02 3 1023 particles). The quantity R is a number called the molar (universal) gas constant and has a value of 8.31 J/(mol?K).

Boyle’s law states that the product of

pressure and volume for a given mass of gas is a constant as long as the temperature does not change.



• Transparency 37



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20.6 Buoyancy of AirIn the last chapter you learned about buoyancy in liquids. All the rules for buoyancy were stated in terms of fluids rather than liquids. The reason is simple enough: the rules hold for gases as well as liq-uids. Consider the dirigible and the fish in Figure 20.15. The physical laws that explain a dirigible aloft in the air are the same that explain a fish “aloft” in water. Archimedes’ principle for air states that an object surrounded by air is buoyed up by a force equal to the weight of the air displaced.

Recall that a cubic meter of air at ordinary atmospheric pressure and room temperature has a mass of about 1.2 kg, so its weight is about 12 N. Therefore any 1-cubic-meter object in air is buoyed up with a force of 12 N. If the mass of the 1-cubic-meter object is greater than 1.2 kg (so that its weight is greater than 12 N), it will fall to the ground when released. If a 1-cubic-meter object has a mass less than 1.2 kg, it will rise in the air. Any object that has a mass less than the mass of an equal volume of surrounding air will rise. Any object less dense than the air around it will rise. A gas-filled balloon, such as the one shown in Figure 20.16, rises in the air because it is less dense than the surrounding air.

When you next see a large dirigible airship aloft in the air, think of it as a giant fish. Both remain aloft as they swim through their flu-ids for the same reason: they both displace their own weights of fluid. When in motion, the dirigible may be raised or lowered by means of horizontal rudders or “elevators.”

CONCEPTCHECK ...

... What causes an object to rise?

FIGURE 20.16 �Everything is buoyed up by a force equal to the weight of the air it displaces.

Two rubber balloons are inflated to the same size, one with air and the other with helium. Which balloon experi-ences the greater buoy-ant force? Why does the air-filled balloon sink and the helium-filled balloon float?Answer: 20.6

think!

FIGURE 20.15 �The dirigible and the fish both hover at a given level for the same reason.


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20.6 Buoyancy of Air

Common Misconception Things float in air for different reasons than things float in water.

FACT The rules of buoyancy for gases are the same as those for liquids.

� Teaching Tip Point out that Archimedes’ principle applies to all fluids, i.e., liquids and gases. Objects immersed or submerged in water are buoyed up because there is greater pressure against the bottom of the object than against the top. This is because the bottom is deeper. Likewise for things buoyed upward by air.

Ask I s atmospheric pressure really greater at shoulder level than at head level? Yes, because shoulder level is deeper in the ocean of air than head level. What evidence of this greater pressure exists? A helium-filled balloon, about the size of a head, is visibly buoyed upward, showing that the atmospheric pressure against the bottom of the balloon, held at shoulder level, is greater than the atmospheric pressure against the top, at head level.

Ask Since clouds are denser than the surrounding air, why don’t they fall from the sky? Ah, they do! They fall as fast as the air below rises. So without updrafts, we’d have no clouds.

Any object less dense than the air around it

will rise.





• Next-Time Questions 20-2, 20-4, 20-6

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20.7 Bernoulli’s PrincipleThe discussion of fluid pressure thus far has been confined to station-ary fluids. Motion produces an additional influence.

Relationship Between Fluid Pressure and Speed Most people think that atmospheric pressure increases in a gale, tornado, or hurricane. Actually, the opposite is true. High-speed winds may blow the roof off your house, but the pressure within air that gains speed is actually less than for still air of the same density. As strange as it may first seem, when the speed of a fluid increases, its pressure decreases. This is true for all fluids—liquids and gases alike.

Consider a continuous flow of water through a pipe. Because water doesn’t “bunch up,” the amount of water that flows past any given section of the pipe is the same as the amount that flows past any other section of the same pipe. This is true whether the pipe wid-ens or narrows. As a consequence of continuous flow, the water in the wide parts will slow down, and in the narrow parts, it will speed up. You can observe this when you put your finger over the outlet of a water hose. As shown in Figure 20.17, this is also apparent when water flows through a narrow part of a brook.

Daniel Bernoulli, a Swiss scientist of the eighteenth century, advanced the theory of water flowing through pipes. The relationship between the speed of a fluid and the pressure in the fluid is described by Bernoulli’s principle. He found that the greater the speed of flow, the less is the force of the water at right angles (sideways) to the direction of flow. The pressure at the walls of the pipes decreases when the speed of the water increases. Bernoulli found this to be a principle of both liquids and gases. Bernoulli’s principle in its simplest form states that when the speed of a fluid increases, pres-sure in the fluid decreases.

FIGURE 20.17 �Because the flow is continuous, water speeds up when it flows through the narrow or shallow part of the brook.

A fluid continues to move at constant vol-ume per unit of time through different cross sections of a pipe or confined regions. This is called the “principle of continuity.”

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392

20.7 Bernoulli’s Principle

Key Terms Bernoulli’s principle, streamline, eddy

Common Misconceptions Atmospheric pressure is greater during a hurricane or tornado.

FACT Atmospheric pressure actually drops during hurricanes and tornadoes.

The faster a fluid moves, the greater is its pressure.

FACT When the speed of a fluid increases, the pressure it exerts decreases.

� Teaching Tip Before discussing Bernoulli’s principle, review kinetic energy, potential energy, and conservation of energy.

Make a beach ball hover in a stream of air coming from the reverse end of a vacuum cleaner.

Do the same with a table tennis ball in the air stream of a hair dryer.

Line a cardboard tube with sandpaper and use it to throw the ball sidearm. The sandpaper will produce the friction to make the ball roll down the tube and emerge spinning—you’ll see that the ball breaks in the correct direction.

DemonstrationsDemonstrations


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Bernoulli’s principle is a consequence of the conservation of energy, although, surprisingly, he developed it long before the con-cept of energy was formalized.20.7 The full energy picture for a fluid in motion is quite complicated. Simply stated, higher speed means lower pressure, and lower speed means higher pressure.

The decrease of fluid pressure with increasing speed may at first seem surprising, particularly if we fail to distinguish between the pres-sure within the fluid and the pressure exerted by the fluid on some-thing that interferes with its flow. The pressure within the fast-moving water in a fire hose is relatively low, whereas the pressure that the water can exert on anything in its path to slow it down may be huge.

Streamlines In steady flow, one small bit of fluid follows along the same path as a bit of fluid in front of it. The motion of a fluid in steady flow follows streamlines, which are represented by thin lines in Figure 20.18 and later figures. Streamlines are the smooth paths, or trajectories, of the bits of fluid. The lines are closer together in the narrower regions, where the flow is faster and pressure is less.

Pressure differences are nicely evident when liquid contains air bubbles. The volume of an air bubble depends on the pressure of the surrounding liquid. Where the liquid gains speed, pressure is low-ered and bubbles are bigger. As Figure 20.18b indicates, bubbles are squeezed smaller in slower higher-pressure liquid.

Bernoulli’s principle holds only for steady flow. If the flow speed is too great, the flow may become turbulent and follow a changing, curling path known as an eddy. In that case, Bernoulli’s principle does not hold.

CONCEPTCHECK ...

... What does Bernoulli’s principle state?

a b


FIGURE 20.18 �Water speeds up when it flows into the narrower pipe. a. The close-together streamlines indicate increased speed and decreased internal pressure. b. The bubbles are bigger in the narrow part because internal pressure there is less.

Pressure inside a fluid is different from the pressure it can exert on anything that changes its momentum!

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Tape together two or three small juice cans that have had both ends removed. Make a soap-detergent mix with a bit of glycerin and let it stand overnight. Dip the tube to form a soap film over the end. To make a lung-sized bubble, take a deep breath and, with your mouth sealed against the nonsoapy end of the tube, exhale and gently blow a bubble. Now dip the tube again and blow a full breath of air into the tube end, with your mouth about 10 cm away from the end. If you are careful, you can blow a bubble as big as your entire upper body! When you blow air into the tube, the moving air is at a lower pressure than the stationary air beside it. The stationary air is drawn into the lower-pressure region (or rather, is pushed in by the surrounding atmosphere). This extra air further inflates the bubble, adding to the amount of air you exhale from your lungs. Very nice!

Bernoulli’s principle in its simplest form

states that when the speed of a fluid increases, pressure in the fluid decreases.


• Concept-Development Practice Book 20-2



• Next-Time Questions 20-3, 20-5


CONCEPTCHECK ...

...CONCEPTCHECK ...

...


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20.8 Applications of Bernoulli’s Principle

Bernoulli’s principle partly accounts for the flight of birds and air-craft. Try blowing air across the top of a sheet of paper, as shown in Figure 20.19. The paper rises because air passes faster over the top of the sheet than below it.

Lift Similarly, the shape and orientation of airplane wings ensure that air passes somewhat faster over the top surface of the wing than beneath the lower surface. As shown by the streamlines in Figure 20.20, pressure above the wing is less than pressure below the wing. Lift is the upward force created by the difference between the air pressure above and below the wing.20.8 Even a small pressure dif-ference multiplied by a large wing area can produce a considerable force. When lift equals weight, horizontal flight is possible. The lift is greater for higher speeds and larger wing areas. Hence, low-speed gliders have very large wings relative to the size of the fuselage. The wings of faster-moving aircraft are relatively small.

Atmospheric pressure decreases in a strong wind. As Figure 20.21 shows, air pressure above a roof is less than air pressure inside the building when a wind is blowing. This produces a lift that may result in the roof being blown off. Roofs are usually constructed to with-stand increased downward loads, the weight of snow for example, but not always for increased upward forces. Unless the building is well vented, the stagnant air inside can push the roof off.

Curve Balls Bernoulli’s principle is partly involved in the curved path of spinning balls. When a moving baseball, or any kind of ball spins, unequal air pressures are produced on opposite sides of the ball. In Figure 20.22b, the streamlines are closer together at B than at A for the direction of spin shown. Air pressure is greater at A, and the ball curves as indicated.

FIGURE 20.21 �In high winds, air pressure above a roof can drastically decrease.

FIGURE 20.20 �Air pressure above the wing is less than the pressure below the wing.

FIGURE 20.19 �The paper rises when you blow air across the top of it.

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20.8 Applications of Bernoulli’s Principle

Key Term lift

� Teaching Tip Point out that although some lift is explained by Bernoulli’s principle, due to the airfoil shape of wings, airplane wings would work without the airfoil. Some model planes have flat wings! The slot that holds such wings is usually cut with an “angle of attack.” In this way, oncoming air is forced downward. Newton’s third law states the rest: If the wing forces air downward, the air simultan-eously forces the wing upward.

� Teaching Tip A neat consequence of Bernoulli’s principle involves the thickness of a firefighter’s hose when water is moving and when it is at rest. When the hose is turned off, but under pressure, the hose is fatter than when it is turned on. The faster the water flows in the tube, the thinner it becomes. That’s because the pressure in the hose drops as water increases in speed.

Trying to explain Bernoulli’s principle in terms of the differences in molecular impacts on the top and bottom surfaces of the wings turns out to be very challenging—especially when experiments show that molecules don’t make impact on the top surface anyway. A thin boundary layer of air is carried in this low-pressure region. This is evidenced by the dust found on the surface of fan blades!


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Boat Collisions Bernoulli’s principle explains why passing ships run the risk of a sideways collision. Water flowing between the ships travels faster than water flowing past the outer sides. Streamlines are closer together between the ships than outside. Hence, water pres-sure acting against the hulls is reduced between the ships. Unless the ships are steered to compensate for this, the greater pressure against the outer sides of the ships forces them together. Figure 20.23 shows a demonstration of this, which you can do in your kitchen sink. Loosely moor a pair of toy boats side by side. Then direct a stream of water between them. The boats will draw together and collide.

Shower Curtains A similar thing happens to a bathroom shower curtain when the shower water is turned on full blast. Air near the water stream flows into the lower-pressure stream and is swept downward with the falling water. Air pressure inside the curtain is thus reduced, and the atmospheric pressure outside pushes the curtain inward (providing an escape route for the downward-swept air). This effect is small compared with the convection produced by temperature differences, but nevertheless, the next time you’re tak-ing a shower and the curtain swings in against your legs, think of Daniel Bernoulli!

CONCEPTCHECK ...

... How is horizontal flight possible?

� FIGURE 20.22Bernoulli’s principle is partly involved in the curved path of a spinning ball. a. The streamlines are the same on either side of a nonspin-ning ball. b. A spinning ball produces a crowding of streamlines.

� FIGURE 20.23 Try this experiment in your sink and watch Bernoulli’s principle in action!

For:

–Visit:Web Code:

Links on Bernoulli’s principle

www.SciLinks.org csn 2008

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� Teaching Tip Anyone who has placed papers on a car seat only to find them blowing out an open window has experienced Bernoulli’s principle. The air rushing outside produces lowered pressure at the window opening. Higher-pressure interior air then rushes out, carrying papers with it. (A similar effect is observed when curtains flap outside an open window on a breezy day or when the top of a convertible car appears to bulge out due to reduced pressure over the top of the roof.)

� Teaching Tip The curving of pitched balls can be more complicated than the text suggests, especially when different surface textures are taken into account. An excellent resource for more on this is Brancazio’s informative book Sport Science.

When lift equals weight, horizontal

flight is possible.



• Problem-Solving Exercises in Physics 10-4

• Transparencies 38, 39



CONCEPTCHECK ...

...CONCEPTCHECK ...

...

Swing a table tennis ball taped to a string into a stream of water. Follow this up with a discussion of the shower curtain in the last paragraph of the chapter.



REVIEW

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For:Visit:Web Code: –

Self-Assessment PHSchool.com csa 2000

Concept Summary ••••••

• Earth’s atmosphere consists of molecules that occupy space and extends many kilo-meters above Earth’s surface.

• Atmospheric pressure is caused by the weight of air, just as water pressure is caused by the weight of water.

• The height of the mercury in the tube of a simple barometer is a measure of the atmospheric pressure.

• An aneroid barometer uses a small metal box that is partially exhausted of air. The box has a slightly flexible lid that bends in or out as atmospheric pressure changes.

• Boyle’s law states that the product of pressure and volume for a given mass of gas is a constant as long as the tempera-ture does not change.

• Any object less dense than the air around it will rise.

• Bernoulli’s principle in its simplest form states that when the speed of a fluid in-creases, pressure in the fluid decreases.

• When lift equals weight, horizontal flight is possible.

Key Terms ••••••••••••••

barometer (p. 386)

aneroid barometer (p. 388)

Boyle’s law (p. 390)

Bernoulli’s principle (p. 392)

streamline (p. 393)

eddy (p. 393)

lift (p. 394)

20.2 960 kg. The volume of air is (200 m2)(4 m) 800 m3. Each cubic meter of airhas a mass of about 1.2 kg, so (800 m3)(1.2 kg/m3) 960 kg (about a ton).

20.5.1 The pressure in the balloon is increased three times. No wonder balloons break when you squeeze them!

20.5.2 Atmospheric pressure can support a col-umn of water 10.3 m high, so the pressure in water due to the weight of the water alone equals atmospheric pressure at a depth of 10.3 m. Taking the pressure of the atmosphere at the water’s surface into account, the total pressure at this depth is twice atmospheric pressure. Unfortunately for the scuba diver, her lungs will tend to inflate to twice their normal size if she holds her breath while rising to the surface. A first lesson in scuba diving is not to hold your breath when ascending. To do so can be fatal.

20.6 Both balloons are buoyed upward with the same buoyant force because they displace the same weight of air. The reason the air-filled balloon sinks in air is because it is heavier than the buoyant force that acts on it. The helium-filled balloon is lighter than the buoyant force that acts on it. Or put another way, the air-filled balloon is slightly more dense than the surround-ing air (principally because it is filled with compressed air). Helium, even somewhat compressed, is much less dense than air.

think! Answers

0


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• TeacherEXPRESS

• Virtual Physics Lab 21

• Conceptual Physics Alive! DVDs Gases


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Check Concepts ••••••

Section 20.1 1. a. What is the energy source for the motion

of gases in the atmosphere? b. What prevents atmospheric gases from

flying off into space?

2. How does the density of gases at different elevations in the atmosphere differ from the density of liquids at different depths?

Section 20.2 3. What causes atmospheric pressure?

4. Why doesn’t the pressure of the atmosphere break windows?

5. What is the mass of a cubic meter of air at 20°C at sea level?

6. a. What is the mass of a column of air that has a cross-sectional area of 1 square cen-timeter and that extends from sea level to the top of the atmosphere?

b. What is the weight of this air column? c. What is the pressure at the bottom of this

column?

7. Is the value for atmospheric pressure at the surface of Earth a constant? Explain.

Section 20.3 8. How does the pressure at the bottom of the

76-cm column of mercury in a barometer compare with the pressure due to the weight of the atmosphere?

9. When you drink liquidthrough a straw, it is moreaccurate to say the liquidis pushed up the strawrather than suckedup the straw. What exactly does the pushing? Explain.

10. Why will a vacuum pump not operate for a well that is deeper than 10.3 m?

Section 20.4 11. The atmosphere does not ordinarily crush

cans. Yet it will crush a can after it has been heated, capped, and cooled. Why?

12. What property of atmospheric pressure is used by an aneroid barometer?

ASSESS0


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ASSESS

Check Concepts 1. a. The sun

b. Gravity

2. Density of a gas varies but density of a liquid remains almost constant.

3. Weight of air

4. The atmospheric pressure doesn’t normally break windows because it acts on both sides of the window.

5. 1.21 kg

6. a. About 1 kg b. About 10 N c. About 10 N/cm3

7. No, air currents and storms cause it to change.

8. Same

9. It is pushed up by atmospheric pressure.

10. Air pressure supports only a 10.3-m column of water.

11. There is a pressure imbalance when the internal pressure is reduced.

12. Atmospheric pressure varies with altitude.



Self-Assessment PHSchool.com csa 2000ASSESS (continued)0

398

Section 20.5 13. When air is compressed, what happens

to its density?

14. A piston in an airtight pump is withdrawn so that the volume of the air chamber is increased five times. What is the change in pressure?

15. When you squeeze an air-filled toy balloon to half size, how does the air pressure inside change?

Section 20.61 6. a. How much buoyant force acts on a 1-N

balloon suspended at rest in air? b. What happens if the buoyant force

decreases? c. What happens if the buoyant force

increases?

Section 20.7 17. When the speed of a fluid flowing in a hori-

zontal pipe increases, what happens to the internal pressure in the fluid?

18. a. What are streamlines? b. Is the pressure greater or less in regions

where streamlines are crowded?

Section 20.8 19. In addition to Bernoulli’s principle, what

other physics explains the lift produced by an airplane wing?

20. Why does a spinning ball curve in flight?

Plug and Chug ••••••

The key equations of the chapter are shown below in bold type.

mV

21. Calculate the density of a gas with a mass of 4.29 kg and a volume of 3.0 cubic meters. Express your answer in kg/m3.

22. Calculate the density of a gas with a mass of 0.00020 kg and a volume of 1.0 liter. Express your answer in kg/m3.

P1V1 P2V2

23. An inflated balloon has internal pressure P1.

Use Boyle’s law to calculate the pressure P2

when the balloon is compressed to half its volume.

24. Use Boyle’s law to calculate the pressure on the same balloon if it instead expands to twice its volume.

FA

P

25. Calculate the lift on a model airplane wing with an area on one side of 100 cm2 and a difference in air pressure above and below the wing of 0.01 N/cm2.


398

13. It increases.

14. The pressure in the piston chamber decreases to 1/5 its former value.

15. The pressure in the balloon doubles.

16. a. 1 N b. The balloon falls. c. The balloon rises.

17. The pressure is reduced.

18. a. The smooth paths that a fluid follows b. Less

19. Newton’s third law

20. There is a pressure imbalance on the spinning ball.

Plug and Chug 21. Density 5 mass/volume 5

4.29 kg/3.0 m3 5 1.43 kg/m3 (The gas is oxygen at 0°C and 1 atmosphere.)

22. 1.0 L 5 1000 cm3 5 1.0 3 10]3 m3; density 5 mass/volume 5 0.00020 kg 4 1.0 3 10]3 m3 5 0.20 kg/m3 (The gas is likely helium.)

23. From P1V1 5 P2V2, P2 5 P1(V1/V2) 5 P1[V1/(1/2V1)] 5 2P1. Pressure is twice its former value.

24. From P1V1 5 P2V2, P2 5 P1(V1/V2) 5 P1(V1/2V1) 5 1/2 P1. Pressure is half its former value.

25. From P 5 F/A, F 5 PA 5 (0.01 N/cm2)(100 cm2) 5 1.0 N.

Think and Explain 26. Unlike water, air and foam

are easily compressed. Near Earth’s surface, atmospheric pressure and air density are greater (and the foam brick is more squashed). At high altitude, where the atmospheric pressure is less, air density is less.


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Think and Explain ••••••

26. We can understand how pressure in water depends on depth by considering a stack of bricks. The pressure below the bottom brick is determined by the weight of the entire stack. Halfway up the stack, the pressure is half as great as it is at the bottom because the weight of the bricks above is half as great. To explain atmospheric pressure, we should consider compressible bricks, like foam rubber. Why is this so?

27. The “pump” in a vacuum cleaner is merely a high-speed fan. Would a vacuum cleaner pick up dust from a rug on the moon? Explain.

28. Which would weigh more—a bottle filled with helium gas, or the same bottle evacu-ated?

29. A steel tank filled with helium gas doesn’t rise in air, but a balloon containing the same helium easily rises. Why?

30. From Table 20.1, which filling would be more effective in making a balloon rise—helium or hydrogen? Why?

31. A helium-filled balloon pulls upward on its string. Your friend says the upward force is evidence that atmospheric pressure is greater at the bottom of the balloon than on the top. Another friend says such a small difference in altitude wouldn’t make a dif-ference in atmospheric pressure. They both look to you for an answer. What do you tell them?

32. Two identical balloons of the same volume are pumped up with air to more than atmo-spheric pressure and suspended on the ends of a horizontal stick that is balanced. One of the balloons is then punctured. Is there a change in the stick’s balance? If so, which way does it tip?

33. How would the density of air at the bottom of a deep mine shaft compare to the den-sity of the atmosphere at the surface of the ground?


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27. No; a vacuum cleaner operates on Earth because the atmospheric pressure pushes dust into the machine’s region of reduced pressure. On the moon, there is no atmosphere and thus no pressure to push the dust.

28. The helium-filled bottle

29. An object will rise only when the buoyant force exceeds the object’s weight. A steel tank of anything weighs more than the air it displaces, so it won’t rise. A helium-filled balloon weighs less than the displaced air and rises.

30. Hydrogen, because it is less dense. (Helium is nevertheless generally used because, unlike hydrogen, it is not flammable.)

31. Agree with the first friend. The bottom of the balloon is deeper in the atmosphere, which gives it a buoyant force.

32. The end of the stick with the punctured balloon tips upward because it is lightened by the amount of air that escapes. There is a loss of buoyant force on the punctured balloon. However, that loss of upward force is less than the loss of downward force because the density of the air in the balloon before it was punctured was greater than the density of the surrounding air.

33. Greater at the bottom; air is more compressed.




400

34. Atmospheric pressure is nicely demonstrat-ed with the pair of hemispheres shown be-low. When placed together, the hemispheres make up a hollow sphere. After a vacuum pump evacuates much of the air inside, a considerable force is needed to separate the hemispheres. Suppose two people find they must pull with 150 N each to separate them. If instead, one end of the sphere is attached to a wall and only one person pulls the other end, how much force would the one person have to supply to separate the hemispheres?

35. Relative to sea level, would it be slightly more difficult or somewhat easier to drink through a straw at the bottom of a deep mine? At the top of a high mountain? Explain.

36. If there were a liquid twice as dense as mer-cury, and if it were used to make a barom-eter, how tall would the column be?

37. Before boarding an airplane, you buy a bag of chips (or any item sealed in an airtight foil package) and, while in flight, you notice that the bag is puffed up. Explain why this occurs.

38. Why do you suppose that airplane windows are smaller than bus windows?

39. Why do your ears “pop” when you ascend to higher altitudes?

40. Small bubbles of air are released by a scuba diver deep in the water. As the bubbles rise, do they become larger, smaller, or stay about the same size? Explain.

41. When you squeeze an air-filled toy bal-loon, its volume decreases. Your friend says that the mass and the density of air inside increase. Do you agree with your friend? Defend your response.

42. Consider a huge, lazily rotating space habi-tat, carrying its own atmosphere. Would a helium-filled balloon “rise” in such a set-ting? Defend your answer.

43. It is easy to breathe when snorkeling with only your face beneath the surface of the water, but quite difficult to breathe when you are submerged nearly a meter, and nearly impossible when you are more than a meter deep (even if your snorkel tube reaches to the surface). Figure out why, and explain carefully.


400

34. 150 N! Remember Newton’s third law?

35. Easier—greater atmospheric pressure; more difficult—less atmospheric pressure

36. Half as high for the same pressure

37. If the chips are sealed in an airtight package at sea level, then the pressure in the package is about 1 atmosphere. Cabin pressure is reduced somewhat for high altitude flying, so the pressure in the package is greater than the surrounding pressure and the package therefore puffs outward.

38. Airplane windows are small because the difference in pressure between the inside and outside surfaces results in large net forces that are directly proportional to the window’s surface area. (Larger windows would have to be proportionately thicker to withstand the greater net force—windows on underwater research vessels are similarly small.)

39. Atmospheric pressure is less so the outward push is greater.

40. Larger; decreasing pressure

41. Agree that the density increases but not the mass. The number of molecules inside the balloon doesn’t change.

42. Yes; the rotating habitat is a centrifuge and denser air is “thrown to” the outer wall (the floor). Air pressure would vary and the highest pressure would be at the floor and the lowest pressure would be toward the hub. The balloon would be buoyed to the region of less pressure and “rise” toward the hub.


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CHAPTER 20 GASES 401CHAPTER 20 GASES 401

44. An inflated balloon sufficiently weighted with rocks will sink in water.

a. What will happen to the size of the bal-loon as it sinks?

b. Compared with its volume at the surface, what volume will it have when it is 10.3 m below the surface?

45. a. Would a balloon rise in an atmosphere where the pressure was somehow the same at all altitudes?

b. Would a balloon rise in the complete absence of atmospheric pressure (for example, at the surface of the moon)?

46. The buoyant force of air is considerably greater on an elephant than on a small helium-filled balloon. Why, then, does the elephant remain on the ground, while the balloon rises?

47. Why is it that when cars pass each other at high speeds on the road, they tend to be drawn to each other?

48. In a department store, an air stream from a hose connected to the exhaust of a vacuum cleaner blows upward at an angle and sup-ports a beach ball in midair. Which is more effective in keeping the ball up—air blowing across the top or air blowing across the bot-tom of the ball?

49. What physics principle underlies the fol-lowing three observations? When passing an oncoming truck on the highway, your car tends to swerve toward the truck. The can-vas roof of a convertible automobile bulges upward when the car is traveling at high speeds. The windows of older passenger trains sometimes break when a high-speed train passes by on the next track.

50. When a steadily flowing gas flows from a larger-diameter pipe to a smaller-diameter pipe, what happens to each of the following?

a. its speed b. its pressure c. the spacing between its streamlines

51. The diameter of a fire hose varies with the flow rate of water inside. The hose may be relatively narrow, and at another time puffed up like a fat snake. In which case is water flowing fast, and when is water hardly flowing at all?


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43. Pressure in your lungs increases as the greater surrounding water pressure compresses your rib cage and lungs. Your diaphragm cannot reduce the pressure in your lungs enough when you are below a meter in depth, so air will not flow from the surface down to you.

44. a. Becomes smallerb. Total pressure is double, so volume is half

45. a. No, it would fall.b. No; no pressure difference, so no buoyant force.

46. The elephant’s weight is much greater than the buoyant force.

47. The pressure between them is reduced. The greater pressure on the far sides of the cars pushes them together.

48. Air blowing across the top because it would reduce pressure above the ball

49. Bernoulli’s principle for all three examples

50. a. Speed increases (so that the same quantity of gas can move through the pipe in the same time). b. Pressure decreases (Bernoulli’s principle). c. The spacing between the streamlines decreases because the same number of streamlines fit in a smaller area.

51. When water is flowing fast in a hose, water pressure against the insides is less and the hose is narrower. When water is at rest, the pressure is greater and the hose diameter bigger.




402

52. You overhear a conversation between two physics types. One says that birds couldn’t fly before the time of Bernoulli. The other says that it was not so. Birds could fly before the time of Bernoulli but couldn’t fly before the time of Newton. Humor aside, what points are they making?

53. Explain how an airplane is able to fly upside down.

Think and Solve ••••••

54. A typical school gym is about 60.0 m × 30.0 m × 10.0 m. Show that the mass ofair in the gym on a 20˚C day is around22,000 kg.

55. The “height” of the atmosphere is about30 km. The radius of Earth is 6400 km. What percentage of Earth’s radius is the height of the atmosphere?

56. The weight of the atmosphere above1 square meter of Earth’s surface is about 100,000 newtons. If the density of the atmo-sphere were a constant 1.2 kg/m3, calculate where the top of the atmosphere would be.

57. Average atmospheric pressure at Earth’s surface is 1.01 × 105 N/m2. Earth’s radius is 6.37 × 106 m. Show that the total weight of Earth’s atmosphere is about 5.15 × 1019 N.

58. A party balloon is squeezed to 2/3 of its initial volume. Show that the pressure in the balloon is increased by 1.5 times.

59. An automobile is supported by four tires inflated to a gauge pressure of 180 kPa. The area of contact of each of the tires (ignor-ing the effects of tread thickness) is 190 cm2

(which means the total area of tire contact is 0.076 m2). Estimate the mass of the car in kilograms.

60. Suppose you have a syringe that contains air but has no needle. You put your thumb over the opening and then squeezed the plunger of the syringe from the 15 mL mark to the 6 mL mark. Show that the pressure in the syringe will then be 250 kPa.

61. A mercury barometer reads 760 mm at sea level. When it is carried to an altitude of 5.6 km, the height of the mercury column is reduced to half its initial value, or 380 mm.

a. What is the air pressure at this altitude relative to sea-level pressure?

b. If the barometer is taken up another 5.6 km to an altitude of 11.2 km, will the height of its mercury column fall another 380 mm and be zero? Why or why not?


402

52. One attributes flight to Bernoulli’s principle, and the other to Newton’s third law.

53. An airplane flies upside down by tilting its fuselage so that there is an angle of attack of the wing with the oncoming air. (It does the same when flying right side up, but then, because the wings are designed for right-side-up flight, the tilt of the fuselage isn’t as great.)

Think and Solve 54. m 5 rV 5

(1.21 kg/m3)(60.0 m 3 30.0 m 3 10.0 m) 5 22,000 kg

55. 30/6400 3 100% 5 0.47%

56. h 5 P/rg 5 100,000 N/m2 4

(1.2 kg/m3 3 10 N/kg) 5 8.3 3 103 m 5 8.3 km

57. F 5 PA 5 (1.01 × 105 N/m2) 3 [4p 3 (6.37 3 106 m)2] 5 5.15 3 1019 N

58. From P1V1 5 P2V2, P2 5 P1(V1/V2) 5 P1[V1/(2/3V1)] 5 1.5P1.

59. 180 kPa 5 wt of car 4 area of tire contact so wt of car 5 (180 kPa)(1 3 103 N/m2) 4 (1 kPa)(0.076 m2 ) 5 13,680 N. W 5 mg so m 5 (13,680 N)/(10 N/kg) 5 1368 kg.

60. From P1V1 5 P2V2, P2 5 P1(V1/V2) 5 (100 kPa) 3 (15 mL)/(6 mL) 5 250 kPa.

61. a. Since the column of mercury has half the height it has at sea level (where it is 760 mm), air pressure is half its sea-level value.b. Air pressure does not decrease at a constant rate the way water pressure does, so it does not decrease as much in the second 5.6 km of altitude change as in the first 5.6 km. At 11.2 km, the mercury column will be shorter but not zero.


11/26/07 12:58:19 PM




CHAPTER 20 GASES 403CHAPTER 20 GASES 403

62. On a perfect fall day, you are hovering at low altitude in a hot-air balloon, accelerating neither upward nor downward. The total weight of the balloon, including its load and the hot air in it, is 20,000 N. Find the weight of the displaced air.

63. Referring to the previous problem, find the volume of the displaced air.

64. In 1982 Larry Walters ascended from his home in Long Beach, California, to an altitude of 4900 m (16,000 ft) after tying 42 helium-filled, 1.9-m diameter weather balloons to his patio chair. Show that the buoyant force on these balloons at sea level would be 1800 N.

65. How many newtons of lift are exerted on the wings of an airplane that have a total area of 100 m2 when the difference in air pressure below and above the wings is 5% of atmospheric pressure?

Activities ••••••

66. Try this in the bathtub or while washing dishes. Lower a glass, mouth downward, over a small floating object as shown. What happens? How deep would the glass have to be pushed to compress the enclosed air to half its volume? (Hint: You can’t do this in your bathtub unless it’s 10.3 m deep!)

67. Place a card over the open top of a glass filled to the brim with water, and invert it. What happens? Why? Try turning the glass sideways as shown below.

68. Fill a bottle with water and hold it partially under water so that its mouth is beneath the surface. What happens to the water in the bottle? Explain. How tall would the bottle have to be before water ran out? (Hint: You can’t do this indoors unless you have a ceiling 10.3 m high!)

69. Hold a spoon in a stream of water, as shown. Describe and explain the effect in terms of the differences in pressure.

More Problem-Solving PracticeAppendix F

0382_CP09_SE_CH20.indd 403 11/27/07 11:13:34 AM

403

62. The weight of the displaced air must be the same as the weight supported, since the total force (gravity plus buoyancy) is zero. The displaced air weighs 20,000 N.

63. Since W 5 mg, the mass of the displaced air is m 5 W/g 5 (20,000 N)/(10 m/s2) 5 2000 kg. Since r is m/V, the volume of the displaced air is V 5 m/r 5 (2000 kg) 4 (1.2 kg/m3) 5 1700 m3.

64. Fbuoyant 5 rairVg 5 (1.2 kg/m3)[42 3 4/3p 3

(0.95 m)3](10 N/kg) 5 1800 N

65. F 5 0.05 PA 5 (0.05) 3 (105 N/m2)(100 m2) 5 5 3 105 N

Activities 66. Air pocket shrinks; 10.3 m

67. Air pressure on the card is greater than the water pressure.

68. The bottle acts as a barometer; 10.3 m

69. This illustrates Bernoulli’s principle.


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